The World Wide Web continues to evolve and serve as the infrastructure for carrying massive amounts of multimodal and multisensory observations. These observations capture various situations pertinent to peoples needs and interests along with all their idiosyncrasies. To support human-centered computing that empower people in making better and timely decisions, we look towards computation that is inspired by human perception and cognition. Toward this goal, we discuss computing paradigms of semantic computing, cognitive computing, and an emerging aspect of computing, which we call perceptual computing. In our view, these offer a continuum to make the most out of vast, growing, and diverse data pertinent to human needs and interests. We propose details of perceptual computing characterized by interpretation and exploration operations comparable to the interleaving of bottom and top brain processing. This article consists of two parts. First we describe semantic computing, cognitive computing, and perceptual computing to lay out distinctions while acknowledging their complementary capabilities. We then provide a conceptual overview of the newest of these three paradigms--perceptual computing. For further insights, we focus on an application scenario of asthma management converting massive, heterogeneous and multimodal (big) data into actionable information or smart data.